Those are toucanets but I don't remember which exact species. It's illegal to possess native birds, but just about anything that's non-native is fair game as long as it's captive bred or imported legally. So toucanets are OK as long as they weren't poached and smuggled.

Myers parrots aren't big birds so I doubt that they'd be able to chew their way out of a cage with budgie-style bars. They would have an advantage in a fight with a cockatiel though because of the bigger beak. They're somewhat heavier than the average cockatiel too.